There are many medical conditions that degrade the vision of a patient's eye. For instance, cataracts can cause the natural lens of an eye to become opaque. Fortunately, in many of these cases, the natural lens of the eye may be removed surgically and replaced with an intraocular lens, thereby restoring the vision of the eye.
Typically, the power required of the intraocular lens is determined by the properties of the patient's eye, which can include one or more refractive indices, curvatures, and/or distances. Any or all of these properties may be measured for a particular patient, so that a selected power for the intraocular lens matches the power required for a particular eye to within a particular tolerance, such as 0.25 diopters, 0.5 diopters, or 0.75 diopters, depending upon the patient's condition, the type of lens, and other factors.
In some cases, a particular cornea may have a rotational asymmetry that imparts astigmatism onto light that is transmitted through it. The astigmatism degrades the vision of the eye, and cannot be corrected by adjusting the power of the lens. In these cases, the intraocular lens may provide additional correction if it has a similar but opposite amount of astigmatism. Then, the astigmatism of the lens may cancel or reduce the astigmatism of the cornea, and the light reaching the retina of the eye may have reduced astigmatism and, therefore, may have improved vision. For example, an intraocular lens for an astigmatic patient might correct the astigmatism to within a tolerance of about 0.75 diopters.
In practice, there are difficulties with an equal-but-opposite astigmatism correction. In particular, there may be some residual astigmatism left in the eye, caused by, for example, a rotational misalignment between the astigmatic axis of the cornea and the astigmatic axis of the corrective intraocular lens. This rotational misalignment and its effects are shown in greater detail in the text that follows, and in FIGS. 1 and 2.
FIG. 1 is a schematic drawing of a lens pupil in the presence of astigmatism. Strictly speaking, this is astigmatism balanced by defocus so that RMS wavefront error is minimized In terms of wavefront error, FIG. 1 has a given amount of astigmatism W22 with an additional amount of defocus W20 given by W20=−W22/2. In terms of Zernike polynomials, FIG. 1 has a given amount of astigmatism corresponding to the fifth and/or sixth Zernike polynomial terms, depending on the orientation of the astigmatism; in FIG. 1 the fourth Zernike term, corresponding to defocus, is zero.
The wavefront contour map 1 (labeled as “1”) shows contours of equal phase in the pupil. In one direction, in this case the direction denoted by angle θ, the wavefront shows a negative curvature. In a direction perpendicular to that denoted by θ, the wavefront shows a positive curvature. At +/−45° degrees to θ, the wavefront is essentially flat.
For this document, the wavefront contour map 1 may be represented more simply by two equivalent schematic representations 2 and 3 (labeled as “2” and “3”, respectively). Element 2 shows the pupil having a particular amount of astigmatism, denoted by +A, with an orientation denoted by θ. Note that the parallel lines in element 2 act as a guide for the viewer that show the orientation angle of the astigmatism, are not contours of equal phase. The “+” signs show regions of increasing phase in the pupil. Another representation, substantially equivalent to element 2, is element 3, in which an equal but opposite amount of astigmatism, denoted by −A, is oriented at 90° to that in element 2.
Using the drawing conventions of FIG. 1, FIG. 2 shows the effects of a rotational misalignment of a known lens that corrects for the astigmatism of a particular cornea. The circles in FIG. 2 represent the pupil area of the eye. The pupils are shown for simplicity as being circular, but they may include elongations or deformations. In general, the pupil areas correspond to physical locations on the anterior and/or posterior surfaces of the intraocular lens, so that the center of the pupil corresponds to the center of the lens surfaces, the edge of the pupil corresponds to the edge of the lens surfaces, and so forth.
The leftmost circle represents the astigmatism of the cornea of a particular patient's eye. The cornea astigmatism may have any particular orientation in the eye, and may deviate significantly from horizontal or vertical. In FIG. 1, the orientation of the cornea astigmatism is represented by an angle θ.
In practice, the magnitude of astigmatism is typically reported in power, usually in diopters. Alternatively, astigmatism may be reported as an axial separation between two foci, although this is seldom done for the optics of the eye. As a further alternative, astigmatism may be reported in terms of wavefront error. The power error, the axial separation and the wavefront error may all be related simply to each other, and all are substantially equivalent for the purposes of this discussion. In FIG. 2, the magnitude of the cornea astigmatism is denoted by an amount −A. The cornea, therefore, has an astigmatism that can be represented by its magnitude (“−A”) and its orientation (“θ”). 
A known intraocular lens is shown schematically in the middle circle of FIG. 2. The lens itself has an equal and opposite amount of astigmatism as the cornea, which is denoted by the value +A. If this lens were to be implanted in the eye with its astigmatism precisely oriented to that of the cornea, then the corneal astigmatism would be completely or nearly completely cancelled. However, there is usually a small angular error in the orientation that arises during the implantation surgery, which is denoted in FIG. 2 as δ, so that the astigmatism of the lens is oriented at angle θ+δ after implantation. This angular error may be kept as small as possible, but may be limited in practice by the skill of the surgeon. While more skilled surgeons may be able to achieve a δ of about 5 degrees, less skilled surgeons may have difficulty meeting this value and may implant lenses with larger angular errors than 5 degrees.
Mathematically, it is found that the astigmatism of the cornea (amount −A, orientation θ), plus the astigmatism of the rotationally misaligned lens (amount +A, orientation θ+δ), results in a residual astigmatism with magnitude 2A sin δ, oriented at 45° to the angle (θ+δ/2). It is instructive to provide a numerical example of this 2A sin δ quantity, to illustrate the magnitudes of residual astigmatism that may result from angular misalignment of the lens.
Consider a cornea that has 2 diopters of astigmatism, and a lens that has 2 diopters (of the opposite sign) of astigmatism. If the lens is implanted with an angular error δ of 5 degrees, which is a rather tight tolerance for a surgeon, then the residual astigmatism is (2)(2 diopters)(sin 5°)=0.35 diopters. For a looser tolerance of 10 degrees, the residual astigmatism is (2)(2 diopters)(sin 10°)=0.7 diopters. A typical threshold for astigmatism is 0.25 diopters, so that if the light reaching the retina has less than 0.25 diopters of astigmatism, then the astigmatism does not significantly degrade the vision of the eye.
As a result, the residual astigmatism in the eye may impose a prohibitively tight tolerance on the angular orientation of the lens during implantation, resulting in a tedious and expensive implantation procedure. Accordingly, there exists a need for an intraocular lens having a reduced angular orientation tolerance.